Laboratory Prototype of a Launcher Device by Electromagnetic Propulsion using Superconducting Materials

Ricardo Miguel Ramos Almeida Electrical Engineering Department Instituto Superior Técnico, UTL Lisbon, Portugal

Abstract — This paper discusses the design and construction of a This paper addresses the development of a linear electric linear electromagnetic propulsion system that makes use of the launcher device based on the characteristic of a diamagnetic property submitted by the diamagnetic superconducting YBCO superconducting, considering the linear electromagnetic materials. This system consists of two parts: the excitation field propulsion technology [4] [5] [7] as the most suitable for this system (fixed structure), consisting of several independent application. magnetic circuits aligned, and the vehicle (mobile system), where it was used a structure with wheels on rails, where a block YBCO A. Main systems of linear electromagnetic propulsion (Yttrium barium copper oxide) superconducting material is The and are the two main linear inserted. electromagnetic propulsion systems. The railgun system [8] [9] The operation of the implemented propulsion system is based [10] [12] [15] is based on the principle of the homopolar motor, on creating a traveling magnetic wave in the excitation field and characterized by two conducting current rails and also a system, synchronous with the position of the vehicle which the conducting current material projectile. The flowing current in interaction between the produced by each vehicle the system generates in the vehicle a magnetic field with a and the superconducting material in, due to the Meissner effect, vertical direction, which combined with the gives rise to an impulse on the vehicle in synchronism with its displacement. through the vehicle gives rise to a force on the vehicle, pushing It was analyzed the and magnetic field it along the rails. This system has two major problems: heavy distribution of the excitation field system, was finally given the losses by Joule effect and friction in the contact between the resulting force, vehicle’s velocity, impulse and the contribution of vehicle and rail. The system coilgun [11] [12] [13] as depicted each magnetic circuit. in Fig.1, works by establishing a current in each coil in In conclusion, it was verified that the magnetic circuits have sequence along the propulsion system, producing an attractive different contributions depending on the vehicle velocity. The force on the projectile that will move synchronously with the results were compared and analyzed in relation to those provided sequential establishment of the magnetic field. by the developed model for the propulsion system .

Keywords- Linear electromagnetic propulsion system, superconductor, Railgun, Coilgun.

I. INTRODUCTION Man has always been compelled to travel, transporting materials and hurl / throw, in order to survive [1]. Currently the Figure 1 - Diagram of the propulsion system "coilgun" four key technologies for propulsion systems are: [2] [3] [6] This system requires a sub-system that controls the current, − The mechanical propulsion brings together, for instance, but can be changed without losing its characteristics. One of gears and mechanisms that leverage renewable energy the changes can be, for instance, putting the coils perpendicular sources. to the path of the vehicle. − The thermodynamic propulsion combines the steam system B. Forces in superconducting materials and internal combustion engines. The superconductor is a perfect diamagnetic material, − The chemical propulsion includes rockets propulsion and because it blocks drilling along the magnetic field due to a rocket launchers. generated by currents induced in the opposite direction to the external magnetic field. This phenomenon is − The electric propulsion covers various electromechanical defined as Meissner effect [14] [15] [16]. When the systems such as electrothermal propulsion, electrostatic superconductor is surrounded by a not uniform magnetic field, propulsion and electromagnetic propulsion. the Meissner effect originates the removal forces on the

1 surfaces of the superconductor, as illustrated in Fig 2. The C. Theoretical analysis of electromechanical propulsion combination of all forces generates a resulting force. system

1) Implementation of the excitation field system by independent magnetic circuits

Regarding the synchronism required between the vehicle's position and the position of the magnetic field wave generated by the excitation field system, it is achieved in a discreet form by independent magnetic circuits as shown in Fig.4. The propulsion system consists of independent magnetic circuits in sequence and each magnetic circuit is excited in synchronism along the movement of the vehicle, which is caused by the Meissner effect. Figure 2 - Diagram of forces generated by Meissener effect in the superconductor.

z II. MODELLING THE PROPULSION SYSTEM USING x SUPERCONDUCTING MATERIAL B A. Modeling of an ideal solution y The propulsion system consists of two main parts: an excitation field system, responsible for generating a traveling Figure 4 - Representation of the excitation system implemented magnetic field wave (B), synchronous with the motion of the in a discrete form vehicle; and the vehicle itself consists of diamagnetic material (superconducting material) inside and where it operates a force The Fig.5 illustrates the functioning of an independent (F) of magnetic origin, arising from the Meissner effect, magnetic circuit in three dimensions. causing on the vehicle a movement of displacement with a S certain speed. u p e rc o n d B. Concretion of excitation field system . The Fig.3 shows a first substantiation of the excitation field system, which is used two linear in parallel, as the superconducting material in the middle of them. B

F

B Figure 5 - Independent magnetic circuit functioning 2) Defining the Magnetic Field

Figure 3 - Schematic of the propulsion system with Using the software Comsol Multiphysic 3.2 is feasible to continuous linear in excitation and superconductor simulate the behavior of the magnetic field in the magnetic circuit by the finite element method. Using a continuous linear stator allows a propagation of a continuous magnetic field wave along its length origins a Fig.6 presents the simulation results. It shows that there is continuous force and consequently a continuous displacement a higher density of magnetic field inside the circuit than air in the superconductor. However, the implementation of this gap, where there is no superconductor. Thus it’s determined laboratory excitation field system might be complex for a first the magnetic field B in A and B surfaces, where I is current, N study of this kind of system, due to generation of continuous is the number of turns of the winding, f is the thickness of the magnetic field wave and the need for specific measure circuit, δ is the distance between the superconductor and the materials. magnetic circuit, x is the distance already traveled by the vehicle and Rm the magnetic reluctance in A or B surfaces .

2

Observing Fig.8, it’s conclude that there is greater field

density B on the surface A than on the surface B, and there is B f also the highest density of magnetic field in the central area of the surface A, therefore consider useful area (2cm 2) of Fig.9. SupercondutorSuperconductor VistaTop

D C Circuito SuperiorView EnrolamentosWinding Magnetic SuperconductorSupercondutor magnéticoCircuit δ d x A Magnétic Magnétic Ferro Ferro circuit circuit

Vista Front Áreauseful considerada area FrontalView Figure 9 - Representation of useful area ( 2cm 2) at the surface A Figure 6 - Simulation result of the magnetic field in the independent magnetic circuit Table 1 point out the results of the average magnetic field in useful surface area A measured experimentally obtained by N.I N.I B= B = the theoretical model (analytical and simulation). AR (f.x) B R (f.)δ mA mB

Table 1 - Results of field B to 3 x positions Besides the theoretical model of the magnetic field of the x [cm] B [mT] B [mT] B [mT] Error [%] ((B .- B .)/B .*100) magnetic circuit, an experimental prototype was constructed analytical simulated experimental sim exp sim (Fig.7) to validate the model. 1,0 151 121 127 5,0% 2,0 151 125 134 7,2% Supercondutor 3,0 151 124 146 17,7% Analyzing the results presented in Table 1, it’s check that for N=600 and I=4A, the analytical field B is equal to any position x, because the model created is considered uniform throu ghout all the excitation system. On the other hand, the error appears to increase with the position x due to edge effects of the field B, the experimental measurement errors (bad position of the probe and difficult to control the temperature of the superconductor) and the values of magnetic permeability used in the simulation were defined based on some experimental measurements. Windwing Magnetic Circuit 3) Determination of Resulting Force

Figure 7 - Photograph of the prototype The resulting force F is a conjunction of vector forces Fs generated by Meissne r effect in superconducting surfaces. For The magnetic field on the surfaces A and B of the the deduction of analytical force Fs, the useful area of the superconductor were measured w ith a probe of Hall effect, surfaces A and B of the superconductor, it’s used the method of considering x=1cm, x=2cm and x=3cm. Resulting on the Maxwell Stress Tensor [17]. The equation of force Fs has the graph present on Fig.8 tangential component B of the magnetic field B, the 0 is the a) x=1cm magnetic permeability of air and S is the useful area of the 4 Surface A 2 Surface B surfaces A and B. 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 B [T] 2 Vertical distance [cm] distance Vertical ≈ B b) x=2cm Fs .S 4 µ Surface A 2 0 2 Surface B 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 B [T] To complete the theoretical force model it’s used the Vertical distance [cm] distance Vertical Maxwell Stress Tensor model of Comsol Multiphysics and c) x=3cm 4 calculated the resulting force to a I from 2 to 8 Surface A 2 Surface B amps and a distance x of 1 cm to 3.5 cm, in intervals of 0.5 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 cm. B [T] Vertical distance [cm] distance Vertical The previous prototype was developed to confirm the Figure 8 - Graph of the vertical distribution of field B in the theoretical results, a dding wheels and rails, and using a force surfaces A and B of the superconductor sensor to measure the resulting force, as shown in Fig.10.

3

consider only the tangential field B in the calculation of the Vehicle Rail Maxwell Stress Tensor. The resulting force F of the three methods to a current I=7A, along with the position x, as illustrated in Fig.12, x confirm that the analytical method has a significant error. The F other methods show that up to x=2cm the force Fs of the surface B greatly diminishes the force F. On the interval x=[2 Force Sensor 3] cm the resulting force is maximum and constant. In the last

Copper box containing interval, x=[3 3.5] cm, the resulting force returns to decrease the superconductor due to the no uniformity of the magnetic field. Magnetic Circuit Winding Force - x (I=7A) 8 Analytical Force a) 7.5 Simulated Force Experimental Force

7

6.5

F [N] 6

Reflector Wheels 5.5

5

Supercond. 4.5 1 1.5 2 2.5 3 3.5 x [cm]

Copper box Figure 12 - Resulting force F along x diagram, for I=7A

b) c) Figure 10 - a) Picture of the prototype during a test of III. VEHICLE DYNAMIC MODEL strength, b) Picture of the vehicle, c) Picture of the To put the vehicle in motion, it was developed the superconductor prototype shown in Fig.13. Position sensors and the reflector are fundamental in this propulsion system, because they Fig.11 show the graph with the resulting force F synchronized the vehicle and the magnetic field, as explained calculations achieved by the theoretical model (analytical and before in the introduction. It is important to notice that there simulated) and tests on experimental prototype. must be an interval between the circuits because of the Analytical Force dimensions of the windings. a) x=1cm Simulated Force b) x=1,5cm Experimental Force 10 10

5 5 F[N] F [N] Vehicle 0 0 2 3 4 5 6 7 8 2 3 4 5 6 7 8 Position Sensors I [A] I [A] c) x=2cm d) x=2,5cm 10 10 Reflector 5 5 F[N] F[N]

0 0 Superconductor 2 3 4 5 6 7 8 2 3 4 5 6 7 8 I [A] I [A] e) x=3cm f) x=3,5cm Copper box 10 10 rails

5 5 F [N] F [N] Winding 0 0 2 3 4 5 6 7 8 2 3 4 5 6 7 8 I [A] I [A] Magnetic Circuit Figure 11 - Graphs of resulting force from t he analytical Figure 13 - Prototype propulsion system scheme method, simulated and experimental

As the graphs (Fig.11) show above, the resulting force A. Verification of friction between wheels and rail varies quadratically with the current. It seems like , for all situations , the simulated and experimental results have low To develop a theoretical model as experimental model is significant error, however, the analytical results show a high nece ssary to estimate the value of friction between the wheels error ranging between 21% and 32% This discrepancy results and rails. Using the method of the inclined plan e (Fig.14), it from simplifications and considerations made during the achieves a system which intervene only the gravity force Fg deduction of the analytical model, such as a uniform field B, and the frictional force Fa. N is the normal force, g is the the ideality of materials, the contempt of magnetic leakage and gravitational acceleration and α is the angle between the rails and the horizontal plane. Using an ultrasonic sensor is possible

4 to evaluate the vehicle's acceleration during descent Graphic x-v (vehicle mass: 800gr) way and thus determine the friction. 0.8 Experimental velocity Theoretical velocity N 0.7

0.6 Fa V ehicle π/2 -α Fg.sen( α) 0.5 α F .cos( α) 0.4 g Rails v [m/s] Fg 0.3 α 0.2 Figure 14 - Inclined plane scheme 0.1 0 -0.1 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3 The following equation enables to calculate the coefficient x [m] of friction of the system ( βc). g.sen(α ) − dv Figure 16 - Experimental and theoretical velocity graph for a β = dt vehicle with a mass=800gr c g.cos(α ) Graphic x-v (vehicle mass: 1100gr)

Considering that M is the mass of the vehicle and v its Experimental velocity velocity, it has as a theoretical dynamics model of the 0.6 Theoretical velocity propulsion system: 0.5  2 dv =B −β α 0.4  .Sc .g.cos( )  µ 0.3 dt 2M 0

 [m/s] v  dx = 0.2  v  dt 0.1 0

-0.1 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3 B. Experimental tests of position and velocity x [m]

The theoretical dynamic model can be validated by Figure 17 - Experimental and theoretical velocity graph for a comparing the calculated velocity from the model with vehicle with a mass=1100gr experimental velocities achieved from the prototype. With a Graphic x-v (vehicle mass: 1200gr) provided current of 4 amps on the windings, it was considered 0.6 Experimental velocity Theoretical velocity four values for vehicle mass M: 300gr, 800gr, 1100gr and 0.5 1200gr. Using a positioning-time ultrasonic sensor on prototype it 0.4 can be determined the experimental velocity. Thus, it is 0.3 v [m/s] v pointed out on the graphs from Fig.15 to Fig.18, the 0.2 representation of theoretical velocity (o) and experimental 0.1 velocity (blue). Furthermore, the location of magnetic circuits 0 is represented on the abscissa axis. -0.1 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3 The data experimentally obtained by the ultrasonic sensor x [m] had to be developed, due to the sampling frequency. Therefore the data were filtered, then derived (in order to achieve the Figure 18 - Experimental and theoretical velocity graph for a velocity) and finally filtered again. vehicle with a mass=1200gr

Graphic x-v (vehicle mass: 300gr) 1.5 The four previous figures show that the vehicle increases Experimental velocity Theoretical velocity its velocity when it is in the magnetic circuit air gap and decreases velocity when is in the interval between magnetic 1 circuits. Each magnetic circuit provides a different increase of velocity, because the resulting force value is constant in all circuits. When the velocity is increased the vehicle is less time v[m/s] 0.5 in the air gap, and the force is applied for less time, so we have less acceleration and less increase in velocity. There are two possible solutions to this problem, one is build circuits 0 with increasing magnetic sizes along the path, the other is 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3 x [m] creating an increasing intensity of magnetic field along the path, which may be obtained by changing the current or the Figure 15 - Graph of experimental and theoretical velocity for number of turns of the windings. a vehicle with a mass=300gr

5

Considering experimental data, it seems that all graphs Table 2 – Theoretical Unit Force demonstrate theoretical and experimental velocities similar to For ce [N] For ce [N] For ce [N] For ce [N] x=0.07m. On the remaining path, the difference between 1st circuit 2nd circuit 3rd circuit 4th circuit theoretical and experimental velocity will depend on the speed 300gr 1,8 6 1,8 6 1,8 6 1,8 6 of vehicle. Suggesting that there is a reduction of the resulting force caused by currents induced in the superconductor, when 800gr 1,47 1,47 1,47 1,47 it crosses the air gap, creates a magnetic field on opposite 1100gr 1,24 1,24 1,24 1,24 direction to the magnetic air gap, and turns lower the magnetic 1200gr 1,16 1,16 1,16 1,16 field B as well as the resulting force. However, the theoretical model shows acceptable results, Table 3 – Experimental Unit Force especially for lower velocities. Force [N] For ce [N] For ce [N] For ce [N]

1st circuit 2nd circuit 3rd circuit 4th circuit C. Impulse of the vehicle determination 300gr 1,92 0,97 1,13 1,23 The impulse is defined by the movement quantity variation 800gr 1,49 1,29 1,38 1,11 of the vehicle. 1100gr 1,28 1,27 1,06 0,98 If ∆v is the variation on velocity, the impulse I is given by: 1200gr 1,25 1,23 1,25 0,89

I= M. ∆ v

As illustrated on Fig.15 to Fig.18 is possible to determine Theoretical and experimental values of unit force, present the value of the impulse given to vehicle by the propulsion on tables 2 and 3, represent four magnetic circuits of the system, as illustrated in Fig.19. propulsion system and the four vehicle mass values. It seems that the theoretical unit force is constant in the four magnetic 0.8 Theoretical Impulse circuits for a given mass, but on contrary on the experimental Experimental Impulse 0.7 Error unit force it is not.

0.6 Table 4 – Percentage error between the theoretical and 0.5 experimental unit force 0.4 I [N.s] Error [%] Error [%] Error [%] Error [%] 0.3 1st circuito 2nd circuito 3rd circuito 4th circuito 0.2 300gr 3,1 48,0 39,4 33,9 0.1 800gr 1,0 12,0 6,4 24,3 0 300 400 500 600 700 800 900 1000 1100 1200 Vehicle mass [gr] 1100gr 2,9 2,6 14,7 21,0

Figure 19 – Vehicle impulse graph 1200gr 9,1 5,6 7,9 23,5

The graph shows that the impulse is higher for a larger Table 4 shows the percentage error between experimental mass of the vehicle. The error is higher for a smaller mass and theoretical unit force, and is evidence that for any mass, in vehicle and it fades when comparing to the vehicle with larger the first circuit the error value lower than 10% and can be mass. considered a small error, especially for the masses of 300gr, This is the evidence that the error evolution increases when 800gr and 1100gr. In the second and third magnetic circuits we increase as well the vehicle velocity. the error gets higher, however, on the fourth circuit it has the highest value. In sum, these results indicate that the circuits 1) Force exerted by the magnetic circuit on the vehicle where the vehicle goes with higher velocity the error between the experimental and theoretical unit force is superior. It is considered the force exerted on the superconducting The cause of this effect has already been mentioned earlier, magnetic circuit as the unit force Fu that can be defined by: with the increase of vehicle velocity by current induced in the = I superconductor, which generates an induced magnetic field Fu ∆t and decreases the intensity of the magnetic field inside the air gap, reduces the unit force on the conductor. The determination of I in each impulse on the excitation field circuit and the determination of the duration of the vehicle in the air gap ∆t enables to calculate the unit force exerted by each magnetic circuit on the vehicle.

6

Unitary Force (vehicle mass=1100gr) EFERENCES 2 V. R Unitary Theoretical Force 1.8 Unitary Experimental Force [1] Elior de Oliveira Faria, “Histórias dos Transportes 1.6 Terrestres no Mundo”, Universidade Federal do Rio de 1.4 Janeiro, http://www.transitocomvida.ufrj.br/download 1.2 /Hist%F3ria%20dos%20transportes%20terrestres.pdf

1

F[N] [2] Lino Guzzella ; Antonio Sciarretta, “Vehicle Propulsion 0.8 Systems : introduction to modeling and optimization”, 0.6 Springer, segunda edição, 2007. 0.4 [3] Paul A. Czysz e Claudio Bruno “Future Spacecraft 0.2 Propulsion Systems”, Springer, 2009, pp. 11-13. 0 0 0.04 0.07 0.11 0.14 0.18 0.21 0.25 0.3 [4] Rodolfo A. D. Oliveira, A. Leão Rodrigues, “Desenho e x [m] Construção de um Motor Linear de Indução de Baixa Velocidade”, DEE-FCT, Univ. Nova de Lisboa. Figure 20 – Unit Force for a vehicle with a mass=1100gr [5] Davide Sérgio Baptista da Fonseca, “Accionamento Linear de Relutância Variável Comutado para Tracção Eléctrica As an example, Fig.20 illustrates the evolution of both unit Ligeira” Tese de Doutoramento da Univ. da Beira Interior, forces to the mass of 1100gr, disclosing that for lower 2008 velocities, the experimental unit force is similar to the [6] Robert G. Jahn , Edgar Y. Choueiri “Electric Propulsion: theoretical unit force. However, with increasing velocity on Encyclopedia of Physical Science and Technology” Third the third and fourth magnetic circuits, the experimental force Edition, Volume 5 decreases in comparison with the theoretical force. [7] Kurt J. Kloesel, Jonathan B. Pickrel e Emily L. Sayles,“First Stage of a Highly Reliable Reusable Launch System” AIAA SPACE 2009 Conference & Exposition, IV. CONCLUSION Pasadena - California. Regarding the several types of existing propulsion systems, [8] Victor Sung,“Lumped Parameter Modeling of the Ideal in this particularly case, it was designed and built an Railgun: Examining Maximum Electromechanical Energy electromagnetic propulsion system with the excitation system Conversion Efficiency” Rose-Hulman Institute of by independent magnetic circuits, that were set aligned in a Technology, path, including a vehicle with perfect diamagnetic properties, [9] S. Barker, Ben Roberts e outros. “A Power Supply using a superconducting material. This propulsion system Oriented Small-Caliber EML Design Methodology”, Final applies a synchronous magnetic field to the circuit, which with Report to the U.S. Army Research Laboratory, Maryland, the motion of the vehicle, due to the Meissner effect, provides 2005 a repulsive force. [10] Matthew Assey, “General Railgun Function” The magnetic field was analyzed with superconductor in the http://www.matthewmassey.com/ RailgunTheory.pdf air gap existing on the magnetic circuit, as well as the force [11] T. J. Burgess, E. C. Cnare, W. L. Oberkampf, S. G. that causes the magnetic field by the Meissner effect. Beard, and M. Cowan, "The Electromagnetic Theta Gun It was found as a result that the magnetic field has more and Tubular Projectiles", IEEE Transactions on Magnetics, intensity in surface A and B of the superconductor and also on VOL. MAG-18, NO. 1, January 1982 the surface area of 2cm 2. Besides this, the force was not [12] Kolm, Kevin Fine, Fred Williams and Peter constant, it depended on the intensity on the magnetic field Mongeau, “ELECTROMAGNETIC GUNS, and on the superconductor position within the air gap. LAUNCHERS and REACTION ENGINES” The velocity of the vehicle was also examined and it was Massachusetts Institute of Technology, Francis Bitter concluded that each circuit of excitation contribute differently National Laboratory, Cambridge, Massachusetts, for the vehicle’s velocity. Thus, on the first circuit there is a 1980. superior increased of velocity, when comparing with the [13] Wikipédia, a enciclopédia livre. Railgun e Coilgun. fourth circuit, that shows a less velocity increase. [Online] [Citação: 27 de Setembro de 2010.] The theoretical and experimental velocities reveal a small http://en.wikipedia.org/wiki/Railgun e difference between slower velocities, but with the increase of http://en.wikipedia.org/wiki/Coilgun velocities the differential is higher. [14] Bruno Miguel Carones Painho, “Protótipo Laboratorial de Analyzing the impulse and the unit force it can be um Veículo de Levitação Magnética (MAGLEV) com concluded that the theoretical and the experimental model, Utilização de Supercondutores”, Tese de Mestrado have an error that occurred depending on the increasing of Integrado em Eng. Electrotécnica e de Computadores de velocity. Outubro de 2009, DEEC-IST, UTL. In conclusion, the theoretical model sets reasonably well [15] Ricardo Nuno de Brito Barros André, “Protótipo the experimental model, especially for low speeds. Laboratorial de um Veículo de Levitação Magnética (MAGLEV) com Utilização de Supercondutores” Tese de

7

Mestrado Integrado em Eng. Electrotécnica e de Computadores de Setembro de 2007, DEEC-IST, UTL. [16] F. M. Araújo-Moreira, A. J. C. Lanfredi, C. A. Cardoso, W. Maluf, e outros ”O fascinante mundo dos materiais Supercondutores” Revista Univerciência, Brasil, Dezembro 2002. [17] Herbert H. Woodson e James R. Melcher, “Electromechanical Dynamics – Part II: Fields, Forces and Motion”, Robert E. Krieger Publishing Company.

8